Mathematics Asked by user812072 on January 21, 2021
I’ve recently found out that $sum_{n=1}^{infty}frac{1}{n^2+n}$ makes 1, since it becomes $frac{1}{2}, frac{2}{3}$ and so on. After then, I’ve became curious if I do the same thing with the reciprocal of n squared, or $$sum_{n=1}^{infty} frac{1}{n^2}$$ I couldn’t find out the answer. Their sums don’t make a neat form like $frac{a}{a+1}$. Could anyone tell me what it approaches to?
The sum is $pi^2/6$. Euler first figured that out. It's no surprise and no disgrace that you didn't. See https://en.wikipedia.org/wiki/Basel_problem .
Answered by Ethan Bolker on January 21, 2021
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